Yes, dictionaries often give this translation, and for a good reason: historically bonnet was used for lots of different types of headdress, with particular examples being the Glengarry (a hat worn by Scottish soldiers) and the war bonnet (the ceremonial feathered headdress worn by Native Americans). But in modern English the best translation is usually just hat.
It is also used for the bonnet of a car (known as a hood in American English).
Bonaid is the standard modern spelling, although boineid was used in the past.
Is it too pedantic to say that it is not mi as that is nominative/accusative, whereas we need a dative here? It would be like sayin agam translates German bei
mich (accusative) instead of bei mir (dative). It makes a difference to learners because you can always replace mi with am fear (or at least I can) but I cannot say aig am fear. We do not know what the dative of mi is because it never occurs on its own.